Let $\displaystyle (x,y)$ be the common coordinates of $\displaystyle R^{2}$ and $\displaystyle V=R^{2}-\{(x,0):x\le 0\}$. On $\displaystyle V$ the polar coordinates are defined unambiguously for $\displaystyle 0<\theta<2\pi$. Find $\displaystyle \frac{\partial}{\partial{r}}$,$\displaystyle \frac{\partial}{\partial{\theta}}$. Find the relationship between these vectors and $\displaystyle \frac{\partial}{\partial{x}}|$,$\displaystyle \frac{\partial}{\partial{y}}|$.